scholarly journals An analytical solution for slug tracer tests in fractured reservoirs

2005 ◽  
Vol 41 (8) ◽  
Author(s):  
Chao Shan ◽  
Karsten Pruess
Keyword(s):  
Analytical Solution ◽  
Fractured Reservoirs ◽  
Tracer Tests

Novel Analytical Solution and Type-Curves for Lost-Circulation Diagnostics of Drilling Mud in Fractured Formation

2021 ◽  
Author(s):  
Rami Albattat ◽  
Hussein Hoteit
Keyword(s):  
Analytical Solution ◽  
Diagnostic Tool ◽  
Drilling Fluid ◽  
Fractured Reservoirs ◽  
Dimensionless Time ◽  
Type Curves ◽  
Lost Circulation ◽  
Dimensionless Groups ◽  
Drilling Operations ◽  
Mud Loss

Abstract Loss of circulation is a major problem that often causes interruption to drilling operations, and reduction in efficiency. This problem often occurs when the drilled wellbore encounters a high permeable formation such as faults or fractures, leading to total or partial leakage of the drilling fluids. In this work, we present a novel semi-analytical solution and type-curves that offer a quick and accurate diagnostic tool to assess the lost-circulation of Herschel-Bulkley fluids in fractured media. Based on the pressure and mud loss trends, the tool can estimate the effective fracture conductivity, the cumulative mud-loss volume, and the leakage period. The behavior of lost-circulation into fractured formation can be assessed using analytical methods that can be deployed to perform flow diagnostics, such as the rate of fluid leakage and the associated fracture hydraulic properties. In this study, we develop a new semi-analytical method to quantify the leakage of drilling fluid flow into fractures. The developed model is applicable for non-Newtonian fluids with exhibiting yield-power-law, including shear thickening and thinning, and Bingham plastic fluids. We propose new dimensionless groups and generate novel dual type-curves, which circumvent the non-uniqueness issues in trend matching of type-curves. We use numerical simulations based on finite-elements to verify the accuracy of the proposed solution, and compare it with existing analytical solutions from the literature. Based on the proposed semi-analytical solution, we propose new dimensionless groups and generate type-curves to describe the dimensionless mud-loss volume versus the dimensionless time. To address the non-uniqueness matching issue, we propose, for the first time, complimentary derivative-based type-curves. Both type-curve sets are used in a dual trend matching, which significantly reduced the non-uniqueness issue that is typically encountered in type-curves. We use data for lost circulation from a field case to show the applicability of the proposed method. We apply the semi-analytical solver, combined with Monte-Carlo simulations, to perform a sensitivity study to assess the uncertainty of various fluid and subsurface parameters, including the hydraulic property of the fracture and the probabilistic prediction of the rate of mud leakage into the formation. The proposed approach is based on a novel semi-analytical solution and type-curves to model the flow behavior of Herschel-Bulkley fluids into fractured reservoirs, which can be used as a quick diagnostic tool to evaluate lost-circulation in drilling operations.

scholarly journals A General Analytical Solution for Axisymmetric Consolidation of Unsaturated Soil with Impeded Drainage Boundaries

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ming-hua Huang ◽  
Chang Lv ◽  
Zheng-lin Zhou
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Unsaturated Soil ◽  
Fractured Reservoirs ◽  
Improvement Project ◽  
Soil Stratum ◽  
General Analytical Solution ◽  
Consolidation Behavior ◽  
Excess Pore

The consolidation of soil is one of the most common phenomena in geotechnical engineering. Previous studies for the axisymmetric consolidation of unsaturated soil have usually idealized the boundary conditions as fully drained and absolutely undrained, but the boundaries of unsaturated soil are actually impeded drainage in most practical situations. In this study, we present a general analytical solution for predicting the axisymmetric consolidation behavior of unsaturated soil that incorporates impeded drainage boundary conditions in both the radial and vertical directions simultaneously. The impeded drainage boundary is modeled using the third kind boundary, and it can also realize fully drained and absolutely undrained ones by changing the drainage parameter. A general analytical solution is developed to predict the excess pore-air and pore-water pressures as well as the average degree of consolidation in an unsaturated soil stratum using the common methods of eigenfunction expansion and Laplace transform. The newly developed solution is expressed in the product of the terms of time, depth, and radius, which are derived using Laplace transform, usual Fourier, and Fourier-Bessel series, respectively. The eigenfunctions and eigenvalues are evaluated from the impeded drainage boundaries in both radial and depth dimensions. Then, the correctness of the proposed analytical solution is verified against the existing analytical solution for the case of traditional boundaries and against the finite difference solution for the case of general impeded drainage boundaries, and excellent agreements are obtained. Finally, the axisymmetric consolidation behavior of unsaturated soil involving impeded drainage boundaries is demonstrated and analyzed, and the effects of the drainage parameters are discussed. The results indicate that the larger drainage parameter generally expedites the dissipations of the excess pore pressures and further promotes the soil settling process. As the drainage parameter increases, its influence gradually diminishes and even can be neglected when it is larger than 100. The general analytical solution and findings of this study can help for better understanding the axisymmetric consolidation behavior of the unsaturated soil stratum in the ground improvement project with vertical drains as well as the gas-oil gravity drainage mechanism in the naturally fractured reservoirs.

scholarly journals Analytical solution to pressure transient analysis in non-Newtonian/Newtonian fluids in naturally fractured composite reservoirs

2021 ◽  
Author(s):  
Onyinyechi Chizobam Ukwuigwe ◽  
Alpheus O. Igbokoyi
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Fractured Reservoirs ◽  
Direct Synthesis ◽  
Newtonian Fluids ◽  
Naturally Fractured Reservoirs ◽  
Flow Index ◽  
Well Test ◽  
Well Test Analysis ◽  
Naturally Fractured

AbstractDuring polymer flooding into the reservoir using shear-thinning non-Newtonian fluids, an interface exists between the in situ Newtonian crude oil in the reservoir and the injected polymer solution. This paper examines the application of non-Newtonian well test analysis techniques to develop an analytical solution to non-Newtonian/Newtonian fluids with different flow index composite reservoirs for estimating the interface boundary conditions in such reservoirs. Mathematical models were presented and solved analytically using the Laplace transform. The solution was inverted to real domain with the Stehfest algorithm (Stehfest Commun ACM, 1970). Solutions were obtained for three boundary conditions that are infinite acting, constant pressure and no-flow boundaries. New pressure and pressure derivative type curves are developed for naturally fractured reservoirs. A general solution was obtained, which is adaptable to the case of non-Newtonian/Newtonian fluid interface. Numerical examples are used to estimate the radius of investigation, reservoir and power-law flow parameters using type curve matching and Tiab’s direct synthesis technique.

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